x^2+3.2x-9=0

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Solution for x^2+3.2x-9=0 equation:


Simplifying
x2 + 3.2x + -9 = 0

Reorder the terms:
-9 + 3.2x + x2 = 0

Solving
-9 + 3.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 3.2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 3.2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 3.2x + x2 = 0 + 9
3.2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
3.2x + x2 = 9

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = 9 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = 9 + 2.56

Combine like terms: 9 + 2.56 = 11.56
2.56 + 3.2x + x2 = 11.56

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 11.56

Calculate the square root of the right side: 3.4

Break this problem into two subproblems by setting 
(x + 1.6) equal to 3.4 and -3.4.

Subproblem 1

x + 1.6 = 3.4 Simplifying x + 1.6 = 3.4 Reorder the terms: 1.6 + x = 3.4 Solving 1.6 + x = 3.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 3.4 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 3.4 + -1.6 x = 3.4 + -1.6 Combine like terms: 3.4 + -1.6 = 1.8 x = 1.8 Simplifying x = 1.8

Subproblem 2

x + 1.6 = -3.4 Simplifying x + 1.6 = -3.4 Reorder the terms: 1.6 + x = -3.4 Solving 1.6 + x = -3.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -3.4 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -3.4 + -1.6 x = -3.4 + -1.6 Combine like terms: -3.4 + -1.6 = -5 x = -5 Simplifying x = -5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8, -5}

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